It is well-known that carboxylic amides, industrially useful materials, are produced by reaction of carboxylic acids or esters thereof with an amine, which reaction is applicable as a general method of making them, or hydrolysis of the corresponding nitriles. The yield in each of these processes has arrived at an almost satisfactory level owing to the recent development of the technology, but both these processes need long routes from the petroleum chemical raw materials. As an approach to shortening these routes, for instance, a method as disclosed in British Pat. No. 925588 is known, wherein reaction of carbon monoxide with dimethylamine is effected for the production of N,N-dimethylformamide; however, it requires a high pressure as well as troublesome procedure for treatment of the by-products such as formic acid and others. Consequently, development of a simpler and more economical process has been looked for in the industry.